Resolving forces and equilibrium of a particleEdexcel A-Level Maths: Mind map

Exam questions on Resolving forces and equilibrium of a particle

1. A particle of weight 40 N is in equilibrium, supported by two light inextensible strings. String 1 makes an angle of $30^\circ$ with the upward vertical, and string 2 is horizontal.
   String 2 will break if its tension exceeds 30 N. The strings stay at the same angles. Find the greatest weight that this arrangement can support.2 marks
2. A particle of mass 6 kg is placed on a smooth plane inclined at $25^\circ$ to the horizontal. Take $g=9.8\ \text{m s}^{-2}$.
   A horizontal force of magnitude $P$ N, in the vertical plane containing a line of greatest slope and directed towards the plane, holds the particle at rest on the plane. Find $P$.2 marks
3. A particle of mass 2 kg is pulled up a smooth plane inclined at $30^\circ$ to the horizontal by a light string parallel to a line of greatest slope. The tension in the string is 20 N. Take $g=9.8\ \text{m s}^{-2}$.
   Find the acceleration of the particle and the magnitude of the normal reaction between the particle and the plane.3 marks